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Aehle M, Alme J, Gábor Barnaföldi G, Blühdorn J, Bodova T, Borshchov V, van den Brink A, Eikeland V, Feofilov G, Garth C, Gauger NR, Grøttvik O, Helstrup H, Igolkin S, Keidel R, Kobdaj C, Kortus T, Kusch L, Leonhardt V, Mehendale S, Ningappa Mulawade R, Harald Odland O, O'Neill G, Papp G, Peitzmann T, Pettersen HES, Piersimoni P, Pochampalli R, Protsenko M, Rauch M, Ur Rehman A, Richter M, Röhrich D, Sagebaum M, Santana J, Schilling A, Seco J, Songmoolnak A, Sudár Á, Tambave G, Tymchuk I, Ullaland K, Varga-Kofarago M, Volz L, Wagner B, Wendzel S, Wiebel A, Xiao R, Yang S, Zillien S. Exploration of differentiability in a proton computed tomography simulation framework. Phys Med Biol 2023; 68:244002. [PMID: 37949060 DOI: 10.1088/1361-6560/ad0bdd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 11/10/2023] [Indexed: 11/12/2023]
Abstract
Objective.Gradient-based optimization using algorithmic derivatives can be a useful technique to improve engineering designs with respect to a computer-implemented objective function. Likewise, uncertainty quantification through computer simulations can be carried out by means of derivatives of the computer simulation. However, the effectiveness of these techniques depends on how 'well-linearizable' the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications.Approach.This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques.Main results.The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. However, the observed high density and magnitude of jumps was likely to preclude most meaningful uses of the derivatives. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path, and could be reduced in magnitude by a 'fuzzy voxels' approach. The investigated jumps in the MC function arose from local changes in the control flow that affected the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem.Significance.Besides the technical challenges of merely applying AD to existing software projects, the MC and MBIR codes must be adapted to compute smoother functions. For the MBIR code, we presented one possible approach for this while for the MC code, this will be subject to further research. For the tracking subprocedure, further research on surrogate models is necessary.
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Affiliation(s)
- Max Aehle
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Johan Alme
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Johannes Blühdorn
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Tea Bodova
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | | | - Viljar Eikeland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Christoph Garth
- Scientific Visualization Lab, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Nicolas R Gauger
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Ola Grøttvik
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Håvard Helstrup
- Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, NO-5020 Bergen, Norway
| | | | - Ralf Keidel
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Chinorat Kobdaj
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Tobias Kortus
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Lisa Kusch
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Viktor Leonhardt
- Scientific Visualization Lab, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Shruti Mehendale
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Raju Ningappa Mulawade
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Odd Harald Odland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- Department of Oncology and Medical Physics, Haukeland University Hospital, NO-5021 Bergen, Norway
| | - George O'Neill
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Gábor Papp
- Institute for Physics, Eötvös Loránd University, 1/A Pázmány P. Sétány, H-1117 Budapest, Hungary
| | - Thomas Peitzmann
- Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands
| | | | - Pierluigi Piersimoni
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- FSN Department, ENEA, Frascati Research Center, I-00044, Frascati, Italy
| | - Rohit Pochampalli
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Maksym Protsenko
- Research and Production Enterprise 'LTU' (RPE LTU), Kharkiv, Ukraine
| | - Max Rauch
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Attiq Ur Rehman
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Dieter Röhrich
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Max Sagebaum
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Joshua Santana
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Alexander Schilling
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Joao Seco
- Department of Biomedical Physics in Radiation Oncology, DKFZGerman Cancer Research Center, Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Arnon Songmoolnak
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Ákos Sudár
- Wigner Research Centre for Physics, Budapest, Hungary
| | - Ganesh Tambave
- Center for Medical and Radiation Physics (CMRP), National Institute of Science Education and Research (NISER), Bhubaneswar, India
| | - Ihor Tymchuk
- Research and Production Enterprise 'LTU' (RPE LTU), Kharkiv, Ukraine
| | - Kjetil Ullaland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Lennart Volz
- Biophysics, GSI Helmholtz Center for Heavy Ion Research GmbH, Darmstadt, Germany
- Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom
| | - Boris Wagner
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Steffen Wendzel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Alexander Wiebel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - RenZheng Xiao
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- College of Mechanical & Power Engineering, China Three Gorges University, Yichang, People's Republic of China
| | - Shiming Yang
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Sebastian Zillien
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
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